I need help with D and E. ### Hypertension Diagnostic Test Problem Set**Problem Statement:**A new diagnostic test is developed for detecting hypertension. Suppose that 22% of a certain population has hypertension. The sensitivity of the new test is 85% and the specificity is 91%. Suppose that a random subject from this population is selected.**Questions:**a. Find the probability that the subject has hypertension and tests positive.b. Find the probability that the subject does not have hypertension and tests negative.c. Find the probability that the subject has hypertension given the subject tests positive.d. Find the probability that the subject does not have hypertension given the subject tests negative.e. Find the probability that the subject does not have hypertension given the subject tests positive.**Definitions:****Sensitivity (True Positive Rate):** The probability that the test correctly identifies a person with the condition (hypertension) as positive. Given as 85%.**Specificity (True Negative Rate):** The probability that the test correctly identifies a person without the condition (hypertension) as negative. Given as 91%.**Prevalence:** The proportion of the population that has hypertension. Given as 22%.This set of problems requires the application of conditional probability, Bayes' theorem, and understanding of sensitivity and specificity to interpret and solve real-world diagnostic testing scenarios.### Solution Approach:1. **Probability of Hypertension and Testing Positive (Question a)** - Use sensitivity and prevalence. 2. **Probability of No Hypertension and Testing Negative (Question b)** - Use specificity and the complement of prevalence. 3. **Probability of Hypertension Given Positive Test (Question c)** - Use Bayes' Theorem for conditional probability. 4. **Probability of No Hypertension Given Negative Test (Question d)** - Use the complement probability with Bayes' Theorem. 5. **Probability of No Hypertension Given Positive Test (Question e)** - Complement of the probability found in Question c.This problem set enhances understanding of interpreting medical test results and estimating probabilities for practical decision-making based on diagnostic reports.**Note:** No graphs or diagrams are present in the given image.

Given information: The probability that a certain population has hypertension (H) is, P(H) = 0.22…

2. A new diagnostic test is developed for detecting hypertension. Suppose that 22% of a certain population has hypertension. The sensitivity of the new test is 85% and the specificity is 91%. Suppose that a random subject from this population is selected. a. Find the probability that the subject has hypertension and tests positive. b. Find the probability that the subject does not have hypertension and tests negative. c. Find the probability that the subject has hypertension given the subject tests posi- tive. d. Find the probability that the subject does not have hypertension given the subject tests negative. e. Find the probability that the subject does not have hypertension given the subject tests positive.

2. A new diagnostic test is developed for detecting hypertension. Suppose that 22% of a certain population has hypertension. The sensitivity of the new test is 85% and the specificity is 91%. Suppose that a random subject from this population is selected. a. Find the probability that the subject has hypertension and tests positive. b. Find the probability that the subject does not have hypertension and tests negative. c. Find the probability that the subject has hypertension given the subject tests posi- tive. d. Find the probability that the subject does not have hypertension given the subject tests negative. e. Find the probability that the subject does not have hypertension given the subject tests positive.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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I need help with D and E.

### Hypertension Diagnostic Test Problem Set

**Problem Statement:**

A new diagnostic test is developed for detecting hypertension. Suppose that 22% of a certain population has hypertension. The sensitivity of the new test is 85% and the specificity is 91%. Suppose that a random subject from this population is selected.

**Questions:**

a. Find the probability that the subject has hypertension and tests positive.
b. Find the probability that the subject does not have hypertension and tests negative.
c. Find the probability that the subject has hypertension given the subject tests positive.
d. Find the probability that the subject does not have hypertension given the subject tests negative.
e. Find the probability that the subject does not have hypertension given the subject tests positive.

**Definitions:**

**Sensitivity (True Positive Rate):** The probability that the test correctly identifies a person with the condition (hypertension) as positive. Given as 85%.

**Specificity (True Negative Rate):** The probability that the test correctly identifies a person without the condition (hypertension) as negative. Given as 91%.

**Prevalence:** The proportion of the population that has hypertension. Given as 22%.

This set of problems requires the application of conditional probability, Bayes' theorem, and understanding of sensitivity and specificity to interpret and solve real-world diagnostic testing scenarios.

### Solution Approach:

1. **Probability of Hypertension and Testing Positive (Question a)**
- Use sensitivity and prevalence.

2. **Probability of No Hypertension and Testing Negative (Question b)**
- Use specificity and the complement of prevalence.

3. **Probability of Hypertension Given Positive Test (Question c)**
- Use Bayes' Theorem for conditional probability.

4. **Probability of No Hypertension Given Negative Test (Question d)**
- Use the complement probability with Bayes' Theorem.

5. **Probability of No Hypertension Given Positive Test (Question e)**
- Complement of the probability found in Question c.

This problem set enhances understanding of interpreting medical test results and estimating probabilities for practical decision-making based on diagnostic reports.

**Note:** No graphs or diagrams are present in the given image.

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